In terms of computational complexity, this reformulation presents a lower cost because the number of optimization variables are effectively reduced by a factor of \(\text{R}\) . Moreover, the formulation in (REF ) is similar to that of blind deconvolution [1]} (that is, a single source without demixing) with the exception that the true \(\mathbf {Z}^{(*)}\)  to be recovered, albeit being low-rank, is not necessarily rank-one. Still, the results in [1]} can provide probabilistic guarantees for the recovery of the true \(\mathbf {Z}^{(*)}\)  in terms of the matrices \(\mathbf {\Psi }\)  and \(\mathbf {U}\)  associated with the common diffusing graph.
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